# What is the fastest algorithm for computing log determinant?

I am diving into some literature to understand which is the best algorithm for computing the log-determinant of a PSD matrix. So far I have found the following two papers:

We were just wondering if there are other algorithms with better asymptotics, different techniques, or other paper that we should be aware of.

Similar question on Computational Science is this one,

• How large are the matrices of interest? Are they sparse or dense? – Brian Borchers Dec 2 at 13:06
• How accurate do you need the result to be? In particular, do you want the runtime to scale logarithmically with the precision or can you handle polynomial dependence on the estimate precision? – cdipaolo Dec 3 at 0:13